In a cluster best practices are to gather all logs in a single point through an aggregator and analyze them with a dedicated tool. For that reason in K8S, log command is quite basic.
Anyway kubectl logs -h shows some options useful for you:
# Display only the most recent 20 lines of output in pod nginx
kubectl logs --tail=20 nginx
# Show all logs from pod nginx written in the last hour
kubectl logs --since=1h nginx
Some tools with your requirements (and more) are available on github, some of which are:
-
https://github.com/boz/kail
-
https://github.com/wercker/stern